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Wyszukujesz frazę "Jendrol, Stanislav" wg kryterium: Autor


Tytuł:
Unavoidable set of face types for planar maps
Autorzy:
Horňák, Mirko
Jendrol, Stanislav
Powiązania:
https://bibliotekanauki.pl/articles/972016.pdf
Data publikacji:
1996
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
normal planar map
plane graph
type of a face
unavoidable set
cyclic chromatic number
Opis:
The type of a face f of a planar map is a sequence of degrees of vertices of f as they are encountered when traversing the boundary of f. A set of face types is found such that in any normal planar map there is a face with type from . The set has four infinite series of types as, in a certain sense, the minimum possible number. An analogous result is applied to obtain new upper bounds for the cyclic chromatic number of 3-connected planar maps.
Źródło:
Discussiones Mathematicae Graph Theory; 1996, 16, 2; 123-141
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On light subgraphs in plane graphs of minimum degree five
Autorzy:
Jendrol', Stanislav
Madaras, Tomáš
Powiązania:
https://bibliotekanauki.pl/articles/972033.pdf
Data publikacji:
1996
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
planar graph
light subgraph
star
triangulation
Opis:
A subgraph of a plane graph is light if the sum of the degrees of the vertices of the subgraph in the graph is small. It is well known that a plane graph of minimum degree five contains light edges and light triangles. In this paper we show that every plane graph of minimum degree five contains also light stars $K_{1,3}$ and $K_{1,4}$ and a light 4-path P₄. The results obtained for $K_{1,3}$ and P₄ are best possible.
Źródło:
Discussiones Mathematicae Graph Theory; 1996, 16, 2; 207-217
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Lightweight paths in graphs
Autorzy:
Harant, Jochen
Jendrol, Stanislav
Powiązania:
https://bibliotekanauki.pl/articles/255411.pdf
Data publikacji:
2019
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
weighted graph
lightweight path
Opis:
Let k be a positive integer, G be a graph on V(G) containing a path on k vertices, and w be a weight function assigning each vertex v ∈ V(G) a real weight w(y). Upper bounds on the weight [formula] of P are presented, where P is chosen among all paths of G on k vertices with smallest weight.
Źródło:
Opuscula Mathematica; 2019, 39, 6; 829-837
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
An inequality concerning edges of minor weight in convex 3-polytopes
Autorzy:
Fabrici, Igor
Jendrol', Stanislav
Powiązania:
https://bibliotekanauki.pl/articles/972043.pdf
Data publikacji:
1996
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
planar graph
convex 3-polytope
normal map
Opis:
Let $e_{ij}$ be the number of edges in a convex 3-polytope joining the vertices of degree i with the vertices of degree j. We prove that for every convex 3-polytope there is $20e_{3,3} + 25e_{3,4} + 16e_{3,5} + 10e_{3,6} + 6[2/3]e_{3,7} + 5e_{3,8} + 2[1/2]e_{3,9} + 2e_{3,10} + 16[2/3]e_{4,4} + 11e_{4,5} + 5e_{4,6} + 1[2/3]e_{4,7} + 5[1/3]e_{5,5} + 2e_{5,6} ≥ 120$; moreover, each coefficient is the best possible. This result brings a final answer to the conjecture raised by B. Grünbaum in 1973.
Źródło:
Discussiones Mathematicae Graph Theory; 1996, 16, 1; 81-87
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Total edge irregularity strength of trees
Autorzy:
Ivančo, Jaroslav
Jendrol', Stanislav
Powiązania:
https://bibliotekanauki.pl/articles/743612.pdf
Data publikacji:
2006
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
graph labelling
tree
irregularity strength
total labellings
total edge irregularity strength
Opis:
A total edge-irregular k-labelling ξ:V(G)∪ E(G) → {1,2,...,k} of a graph G is a labelling of vertices and edges of G in such a way that for any different edges e and f their weights wt(e) and wt(f) are distinct. The weight wt(e) of an edge e = xy is the sum of the labels of vertices x and y and the label of the edge e. The minimum k for which a graph G has a total edge-irregular k-labelling is called the total edge irregularity strength of G, tes(G). In this paper we prove that for every tree T of maximum degree Δ on p vertices
tes(T) = max{⎡(p+1)/3⎤,⎡(Δ+1)/2⎤}.
Źródło:
Discussiones Mathematicae Graph Theory; 2006, 26, 3; 449-456
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Distance coloring of the hexagonal lattice
Autorzy:
Jacko, Peter
Jendrol', Stanislav
Powiązania:
https://bibliotekanauki.pl/articles/744329.pdf
Data publikacji:
2005
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
distance coloring
distant chromatic number
hexagonal lattice of the plane
hexagonal tiling
hexagonal grid
radio channel frequency assignment
Opis:
Motivated by the frequency assignment problem we study the d-distant coloring of the vertices of an infinite plane hexagonal lattice H. Let d be a positive integer. A d-distant coloring of the lattice H is a coloring of the vertices of H such that each pair of vertices distance at most d apart have different colors. The d-distant chromatic number of H, denoted $χ_d(H)$, is the minimum number of colors needed for a d-distant coloring of H. We give the exact value of $χ_d(H)$ for any d odd and estimations for any d even.
Źródło:
Discussiones Mathematicae Graph Theory; 2005, 25, 1-2; 151-166
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Colouring vertices of plane graphs under restrictions given by faces
Autorzy:
Czap, Július
Jendrol', Stanislav
Powiązania:
https://bibliotekanauki.pl/articles/744449.pdf
Data publikacji:
2009
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
vertex colouring
plane graph
weak parity vertex colouring
strong parity vertex colouring
proper colouring
Lebesgue theorem
Opis:
We consider a vertex colouring of a connected plane graph G. A colour c is used k times by a face α of G if it appears k times along the facial walk of α. We prove that every connected plane graph with minimum face degree at least 3 has a vertex colouring with four colours such that every face uses some colour an odd number of times. We conjecture that such a colouring can be done using three colours. We prove that this conjecture is true for 2-connected cubic plane graphs. Next we consider other three kinds of colourings that require stronger restrictions.
Źródło:
Discussiones Mathematicae Graph Theory; 2009, 29, 3; 521-543
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A note on face coloring entire weightings of plane graphs
Autorzy:
Jendrol, Stanislav
Šugerek, Peter
Powiązania:
https://bibliotekanauki.pl/articles/31232002.pdf
Data publikacji:
2014-05-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
entire weighting
plane graph
face colouring
Opis:
Given a weighting of all elements of a 2-connected plane graph $G = (V,E, F)$, let $f(α)$ denote the sum of the weights of the edges and vertices incident with the face α and also the weight of α. Such an entire weighting is a proper face colouring provided that $f(α) ≠ f(β)$ for every two faces α and β sharing an edge. We show that for every 2-connected plane graph there is a proper face-colouring entire weighting with weights 1 through 4. For some families we improved 4 to 3.
Źródło:
Discussiones Mathematicae Graph Theory; 2014, 34, 2; 421-426
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Maximum Edge-Colorings Of Graphs
Autorzy:
Jendrol’, Stanislav
Vrbjarová, Michaela
Powiązania:
https://bibliotekanauki.pl/articles/31341153.pdf
Data publikacji:
2016-02-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
edge-coloring
r -maximum k -edge-coloring
unique-maximum edge-coloring
weak-odd edge-coloring
weak-even edge-coloring
Opis:
An $r$-maximum $k$-edge-coloring of $G$ is a $k$-edge-coloring of $G$ having a property that for every vertex $v$ of degree $d_G(v) = d, d \ge r$, the maximum color, that is present at vertex $v$, occurs at $v$ exactly $r$ times. The $r$-maximum index $ \chi_r^′ (G) $ is defined to be the minimum number $k$ of colors needed for an $r$-maximum $k$-edge-coloring of graph $G$. In this paper we show that $ \chi_r^′ (G) \le 3 $ for any nontrivial connected graph $G$ and $ r = 1$ or 2. The bound 3 is tight. All graphs $G$ with $ \chi_1^' (G) =i $, $i = 1, 2, 3$ are characterized. The precise value of the $r$-maximum index, $ r \ge 1 $, is determined for trees and complete graphs.
Źródło:
Discussiones Mathematicae Graph Theory; 2016, 36, 1; 117-125
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Facial Rainbow Coloring of Plane Graphs
Autorzy:
Jendroľ, Stanislav
Kekeňáková, Lucia
Powiązania:
https://bibliotekanauki.pl/articles/31343192.pdf
Data publikacji:
2019-11-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
cyclic coloring
rainbow coloring
plane graphs
Opis:
A vertex coloring of a plane graph $G$ is a facial rainbow coloring if any two vertices of $G$ connected by a facial path have distinct colors. The facial rainbow number of a plane graph $G$, denoted by $ rb(G) $, is the minimum number of colors that are necessary in any facial rainbow coloring of $G$. Let $L(G)$ denote the order of a longest facial path in $G$. In the present note we prove that $ rb(T) \le \floor{ 3/2 L(T) } $ for any tree $T$ and $rb(G) \le \ceil{ 5/3 L(G) } $ for arbitrary simple graph $G$. The upper bound for trees is tight. For any simple 3-connected plane graph $G$ we have $ rb(G) \le L(G) + 5 $.
Źródło:
Discussiones Mathematicae Graph Theory; 2019, 39, 4; 889-897
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Light classes of generalized stars in polyhedral maps on surfaces
Autorzy:
Jendrol', Stanislav
Voss, Heinz-Jürgen
Powiązania:
https://bibliotekanauki.pl/articles/744433.pdf
Data publikacji:
2004
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
polyhedral maps
embeddings
light subgraphs
path
star
2-dimensional manifolds
surface
Opis:
A generalized s-star, s ≥ 1, is a tree with a root Z of degree s; all other vertices have degree ≤ 2. $S_i$ denotes a generalized 3-star, all three maximal paths starting in Z have exactly i+1 vertices (including Z). Let be a surface of Euler characteristic χ() ≤ 0, and m():= ⎣(5 + √{49-24χ( )})/2⎦. We prove:
(1) Let k ≥ 1, d ≥ m() be integers. Each polyhedral map G on with a k-path (on k vertices) contains a k-path of maximum degree ≤ d in G or a generalized s-star T, s ≤ m(), on d + 2- m() vertices with root Z, where Z has degree ≤ k·m() and the maximum degree of T∖{Z} is ≤ d in G. Similar results are obtained for the plane and for large polyhedral maps on ..
(2) Let k and i be integers with k ≥ 3, 1 ≤ i ≤ [k/2]. If a polyhedral map G on with a large enough number of vertices contains a k-path then G contains a k-path or a 3-star $S_i$ of maximum degree ≤ 4(k+i) in G. This bound is tight. Similar results hold for plane graphs.
Źródło:
Discussiones Mathematicae Graph Theory; 2004, 24, 1; 85-107
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On Vertices Enforcing a Hamiltonian Cycle
Autorzy:
Fabrici, Igor
Hexel, Erhard
Jendrol’, Stanislav
Powiązania:
https://bibliotekanauki.pl/articles/30146856.pdf
Data publikacji:
2013-03-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
cycle
hamiltonian
1-hamiltonian
Opis:
A nonempty vertex set X ⊆ V (G) of a hamiltonian graph G is called an H-force set of G if every X-cycle of G (i.e. a cycle of G containing all vertices of X) is hamiltonian. The H-force number h(G) of a graph G is defined to be the smallest cardinality of an H-force set of G. In the paper the study of this parameter is introduced and its value or a lower bound for outerplanar graphs, planar graphs, k-connected graphs and prisms over graphs is determined.
Źródło:
Discussiones Mathematicae Graph Theory; 2013, 33, 1; 71-89
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On Maximum Weight of a Bipartite Graph of Given Order and Size
Autorzy:
Horňák, Mirko
Jendrol’, Stanislav
Schiermeyer, Ingo
Powiązania:
https://bibliotekanauki.pl/articles/30146711.pdf
Data publikacji:
2013-03-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
weight of an edge
weight of a graph
bipartite graph
Opis:
The weight of an edge xy of a graph is defined to be the sum of degrees of the vertices x and y. The weight of a graph G is the minimum of weights of edges of G. More than twenty years ago Erd˝os was interested in finding the maximum weight of a graph with n vertices and m edges. This paper presents a complete solution of a modification of the above problem in which a graph is required to be bipartite. It is shown that there is a function w*(n,m) such that the optimum weight is either w*(n,m) or w*(n,m) + 1.
Źródło:
Discussiones Mathematicae Graph Theory; 2013, 33, 1; 147-165
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On long cycles through four prescribed vertices of a polyhedral graph
Autorzy:
Harant, Jochen
Jendrol', Stanislav
Walther, Hansjoachim
Powiązania:
https://bibliotekanauki.pl/articles/743057.pdf
Data publikacji:
2008
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
graph
long cycle
prescribed vertices
Opis:
For a 3-connected planar graph G with circumference c ≥ 44 it is proved that G has a cycle of length at least (1/36)c+(20/3) through any four vertices of G.
Źródło:
Discussiones Mathematicae Graph Theory; 2008, 28, 3; 441-451
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Paths of low weight in planar graphs
Autorzy:
Fabrici, Igor
Harant, Jochen
Jendrol', Stanislav
Powiązania:
https://bibliotekanauki.pl/articles/743525.pdf
Data publikacji:
2008
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
planar graphs
polytopal graphs
paths
weight of an edge
weight of a path
Opis:
The existence of paths of low degree sum of their vertices in planar graphs is investigated. The main results of the paper are:
1. Every 3-connected simple planar graph G that contains a k-path, a path on k vertices, also contains a k-path P such that for its weight (the sum of degrees of its vertices) in G it holds
$w_G(P): = ∑_{u∈ V(P)} deg_G(u) ≤ (3/2)k² + (k)$
2. Every plane triangulation T that contains a k-path also contains a k-path P such that for its weight in T it holds
$w_T(P): = ∑_{u∈ V(P)} deg_T(u) ≤ k² +13 k$
3. Let G be a 3-connected simple planar graph of circumference c(G). If c(G) ≥ σ| V(G)| for some constant σ > 0 then for any k, 1 ≤ k ≤ c(G), G contains a k-path P such that
$w_G(P) = ∑_{u∈ V(P)} deg_G(u) ≤ (3/σ + 3)k$.
Źródło:
Discussiones Mathematicae Graph Theory; 2008, 28, 1; 121-135
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł

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